Philippe Jorion's

Orange County Case:

Using Value at Risk
to Control Financial Risk

Summary

The purpose of this case is to explain how a municipality can
lose $1.6 billion in financial markets.
The case also introduces the concept of "Value at Risk" (VAR),
which is a simple method to express the risk of a portfolio.
After the string of recent derivatives disasters,
financial institutions, end-users,
regulators, and central bankers are now
turning to VAR as a method to foster stability in financial markets.
The case illustrates how VAR could have been applied to the Orange
County portfolio to warn investors of the risks they were incurring.

Citron was able to increase returns on the pool by investing in
derivatives securities and leveraging the portfolio to the hilt.
The pool was in such demand due to its track record that Citron had
to turn down investments by agencies outside Orange County.
Some local school districts and cities even issued short-term taxable
notes to reinvest in the pool (thereby increasing their leverage even
further).
This was in spite of repeated public warnings, notably by John Moorlach,
who ran for Treasurer in 1994, that the pool was too risky.
Unfortunately, he was widely ignored and Bob Citron was re-elected.

The investment strategy worked excellently until 1994, when the Fed
started a series of interest rate hikes that caused severe losses to
the pool. Initially, this was announced as a ``paper'' loss.
Shortly thereafter, the county declared bankruptcy and decided to
liquidate the portfolio, thereby realizing the paper loss.
How could this disaster have been avoided?

The portfolio leverage magnified the effect of movements
in interest rates.
This interest rate sensitivity is also known as duration.
2.1 Define duration

The duration was further amplified by the use of structured notes.
These are securities whose coupon, instead of being fixed, evolves
according to some pre-specified formula.
These notes, also called derivatives, were initially blamed for the
loss but were in fact consistent with the overall strategy.

Citron's main purpose was to increase current income by exploiting the
fact that medium-term maturities had higher yields than
short-term investments.
On December 1993, for instance, short-term yields were less than 3%,
while 5-year yields were around 5.2%.
With such a positively sloped
term structure of interest rates, the tendency may be to increase
the duration of the investment to pick up an extra yield.
This boost, of course, comes at the expense of greater risk.
Plot the term structure on December 1993
(Figure 2).
Display term structure of interest rates as of last week:
Bloomberg.

Perhaps the most notable of
private-sector initiatives toward better risk management is that of
J.P. Morgan, which unveiled its RiskMetrics system in October 1994.
Forecasts of risk and correlations for more than 400 assets
were posted daily on the web site.
This allowed users to compute a portfolio VAR using
the Delta-Normal method based on a 95% confidence level over a daily or
monthly horizon.

There is a growing army of vendors who provide software ranging from
Excel add-ons to million-dollar firm-wide risk management systems.
For instance, visit the sites of
Algorithmics ,
MSCI,
MSCI RiskMetrics,
and
Sungard Trading and Risk Systems.
Among consultants,
Capital Market Risk Advisors
are well known.
The New York consulting firm was hired November 3, 1994, to
dissect the Orange County portfolio.
Within a week, CMRA warned the county that the pool had already lost
$1.5 billion.
The firm now specializes in the valuation of complex portfolios, and in
"financial forensics"--analyzing sources of financial losses.

There is even an association of risk management professionals, the
Global Association of Risk Professionals,
which provides a forum for the exchange of information and
education in the area of financial risk management.
GARP administers the "Financial Risk Manager" certification upon
successful completion of an examination.
For links to risk management sites, visit the following address:
Barry Schachter.

(1) Duration approximation.
The effective duration of the pool was reported by the state
auditor as 7.4 years in December 1994.
This high duration is the result of two factors:
the average duration of individual securities of 2.74 years (most of the
securities had a maturity below 5 years), and the leverage of the
portfolio, which was 2.7 at the time.
In 1994, interest rates went up by about 3%.
Compute the loss predicted by the duration approximation and compare
your result with the actual loss of $1.64 billion.

(2) Computation of portfolio VAR.
(2) The yields data file
contains 5-year yields from 1953 to 1994.
Using this information and the duration approximation, compute the
portfolio VAR as of December 1994.
Risk should be measured over a month at the 95% level.
Report the distribution and compute the VAR:
- using a normal distribution for yield changes (Delta-Normal method),
and
- using the actual distribution for yield changes (Historical-Simulation
method).
Compare the VAR obtained using the two methods.Download the "yields.xls" file.

(3) Interpretation of VAR.
- Convert the monthly VAR into an annual figure.
Is the latter number consistent with the $1.6 billion loss?
- From December 1994 to December 1995, interest rates fell from
7.8% to 5.25%. Compute the probability of such an event.
- It seems that both in 1994 and 1995, interest rate swings were
particularly large relative to the historical distribution.
Suggest two interpretations for this observation.

Advanced (1)
Compute a time-varying volatility of changes in yields using the
RiskMetrics approach to see if the recent volatility is abnormally high.
The exponential model (as used in Riskmetrics) is:

Var[dy(t)] = Var[dy(t-1)] * k + [dy(t-1)*dy(t-1)]*(1-k)

where Var[dy(t)] is the "conditional," predicted variance for time
t and k is the "decay" factor, usually selected as 0.97
for monthly data.
The model states that the variance forecast is a combination of the
previous month forecast and of the latest squared innovation.
For the starting value of the variance (at time t=0), use
the average variance over the whole period.
Compute the monthly volatility forecast (the square root of Var[dy(t)])
and discuss whether
recent interest rates swings are explained by elevated volatility.

Advanced (2)
Next, we check whether the assumption of a
conditional normal distribution seems adequate for changes in yields.
Compute the number of exceptions at the 1-tailed 95% level, using the
monthly volatility forecast just computed and the actual increase in
yield.
Test whether the number of exceptions is in line with what was expected.
(For the exception test,
you can use the normal approximation to the binomial distribution.
Also, be careful to match the volatility forecast with the subsequent
change in yield.)

Really Advanced (Optional)
The historical simulation approach assumes that changes in
monthly yields have an independent, identical distribution (i.i.d.)
The issue is whether this assumption is appropriate:
- Consider now a model with mean-reversion in the mean, such as the
Vasicek model (if seen in the fixed-income course).
Estimate the model, test whether mean reversion seems significant, and
evaluate VAR in the context of this new model.
Does monthly VAR change? What about annual VAR?
- Estimate a GARCH model for the change in yield and compare the
forecasts to that of the EWMA model.

(4) Hedging.
- On December 31, 1994, the portfolio manager decides
not to liquidate the portfolio,
but simply to hedge its interest rate exposure.
Develop a strategy for hedging the portfolio,
using (i) interest rate futures, (ii) interest rate swaps,
and (iii) interest rate caps or floors.
For each strategy, describe the instrument and whether you should take a
long or short position.
- On that day, the March T-bond futures contract closed at 99-05.
The contract has notional amount of $100,000.
Its duration duration can be measured by that of the
Cheapest-To-Deliver (CTD) bond, which is assumed to be 9.2 years.
Compute the number of contracts to
buy or sell to hedge the Orange County portfolio.
- This contract has typical trading
volume of 300,000-400,000 contracts daily.
Verify with recent volume data at the
Chicago Board of Trade (CBOT).
Would it have been possible to put a hedge in place in one day?
- Assuming that futures can be sold in the required amount,
would the resulting portfolio be totally riskless?

The county, fortunately, fared much better than had been feared.
Disaster was narrowly avoided as schools were paid back just enough to
avoid default; the county was able to extend its debt over 20 years.
Perhaps the greatest help came from the private sector, in the form of a
booming economy leading to greater sales tax receipts and payments by
the State.

Since then, the county has filed a recovery plan centered on a
$800 million bond issue,
in which creditors would be fully repaid.
Some county expenses were cut, or transferred to other agencies.
Investors in the pool (cities, schools, agencies and the county
itself), however, are still facing a $800 million shortfall.

It is unlikely the $1.6 billion loss will ever be recovered.
So far, the county has settled a $2 billion lawsuit against Merrill
Lynch, its principal broker, for $437 million. (Incidentally, this
number is very close to the fall in the market value of Merrill stock
on the day the bankruptcy was announced.)
The county has recovered so far
$650 million, a far cry from the $1.6 billion loss.Show update on lawsuits

The municipal bond market was also badly hit by the bankruptcy.
Municipal investments, who were supposed to be guaranteed by the
``full faith and credit'' of the issuer, suddenly appeared vulnerable to
default.
Munis generally dropped in price relative to Treasuries, which in
effect raises the cost of capital for all municipalities around the
country.

Additional lessons can be learned from this exercise.
Had value at risk been measured before 1994,
the Orange County fiasco could very well have been avoided.
It is fair to say that, had the Treasurer announced that
there was a 5 percent chance of losing more than $1.1 billion
over a year, many investors would have thought twice about rushing
into the pool.
In addition, investors would not have the excuse that they did not
know what they were getting into, which would have limited the rash of
ensuing lawsuits.

John Moorlach, the new Treasurer until 2006, has instituted new
investment policies
for the investment pool.
Thereafter,
Moorlach was elected to the Board of Supervisors.

Read the full account of the Orange County disaster, Big Bets Gone Bad:
Derivatives and Bankruptcy in Orange County,
published by Academic Press (September 1995).

In response to billion-dollar losses (Orange County, Barings,
Daiwa, Metallgesellschaft...), the financial industry is turning to
Value at Risk (VAR) as a method to control market risks.

Professor Jorion wrote the first book on VARValue at Risk: The New Benchmark for Controlling Market Risk,
published by Irwin Professional (July 1996).
The book has been translated into Chinese, Hungarian, Japanese, Korean, Polish,
Portuguese, and Spanish.
It has been called an "industry standard".
A new edition was published in 2006.

To learn more about risk management, read the
Financial Risk Manager (FRM) Handbook.
This is the official book for the FRM examination organized by the
Global Association of Risk Professionals (GARP).
This Handbook provides the core body of knowledge for financial risk
managers.
A new edition was published by Wiley in 2010.